On the system of Pell equations \n \n \n \n $$x^2-(a^2b^2 {\\pm } a)y^2=1$$\n \n \n \n x\n 2\n \n -\n \n (\n \n

Abstract

In this paper, we consider the title simultaneous Pell equations, where $$a\\ge 2,b \\ge 1$$ a ≥ 2 , b ≥ 1 are positive integers and p is an odd prime. Particularly, we give all the solutions when $$2\\le a\\le 1000$$ 2 ≤ a ≤ 1000 and $$1\\le b\\le 1000$$ 1 ≤ b ≤ 1000 .